Inter-Domain Gaussian Processes with Arbitrary Mean Functions in Factor Graphs

Abstract

The modeling flexibility and expressivity of inter-domain Gaussian processes, enabled by applying arbitrary linear operators to a latent Gaussian process, is significant and desirable in robotics and probabilistic numerics communities. However, inter-domain Gaussian processes have not yet been available in a probabilistic message-passing formulation. In this paper, we formalize how to enable inter-domain observations for Gaussian processes in a variational message-passing framework. We develop a decoupled inter-domain variational sparse Gaussian process (dID-VSGP) model for univariate latent Gaussian processes with arbitrary mean functions, and derive the mean-field variational message-passing update rules that allow inference in this model. We validate our derivations in a shape exploration and modeling task, and by solution to a linear stochastic partial differential equation representative of physics-informed exploration. We confirm that our message-passing implementation maintains the same scaling complexity as the VSGP analytical solution. Our results further unify the analytical and message-passing approaches to variational inference and enable inter-domain observations in factor-graph Gaussian processes.

Alex Ledbetter

PhD student

I am a PhD student working jointly under EE/BIASlab, ME/Reshape Lab, and ME/Neuromorphic Engineering groups to enable embodied AI for continuous human-like learning.

Hoang Minh Huu Nguyen

Former PhD student

I am a PhD candidate at the Signal Processing Systems group in TU Eindhoven working on Bayesian Machine Learning.

Thijs van de Laar

Assistant professor

I am an assistant professor at BIASlab, where I work on artificial agents that learn to control themselves in uncertain environments. I take inspiration from physics and neuroscience, and develop theory and (software) tools that allow for efficient, real-time interaction.